In this study, we are committed to a structured investigation of differentially private distributed online problems on specialization over a dynamic environment. To begin with, we formulate a differentially private stochastic dual-averaging distributed online algorithm in a generic form, named as DPSDA. We first inject the Laplace noise to perturb the dual variables so that the algorithm has the same output for the execution of two adjacent datasets (cf. Definition 1), which in turn makes it infeasible for the attacker to infer the true data. Then the Nesterov's dual-averaging subgradient method [1]} is adopted in DPSDA as a learning subroutine. As far as we know, DPSDA is the first formal framework of differentially private distributed online learning on specialization.
